What sort of exercise/stretching should I do to build strength for aerial work?
The best way to get strong enough to do aerial work is to do aerial work!
Other things you can do to build upper body and core strength include: pull-ups, bent-arm hangs, Pilates-style abdominal work, yoga, and rock climbing.
In terms of stretching, focus on shoulders, hamstrings, and low back. Working on your straddles and splits is very helpful, but only stretch them when your muscles are warmed up!